The basic principles and techniques for electromagnetic logging for earth formations are well known. For example, induction logging to determine the resistivity (or its inverse, conductivity) of earth formations adjacent a borehole has long been a standard and important technique in the search for and recovery of subterranean petroleum deposits. In brief, a transmitter transmits an electromagnetic signal that passes through formation materials around the borehole and induces a signal in ore or more receivers. The amplitude and/or phase of the receiver signals are influenced by the formation resistivity, enabling resistivity measurements to be made. The measured signal characteristics and/or formation properties calculated therefrom are recorded as a function of the tool's depth or position in the borehole, yielding a formation log that can be used by analysts.
Note, however, that the resistivity of a given formation may be isotropic (equal in all directions) or anisotropic (unequal in different directions). In electrically anisotropic formations, the anisotropy is generally attributable to fine layering during the sedimentary build-up of the formation. Hence, in a formation coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities RX and RY in directions x and y, respectively, tend to be the same, but resistivity Rz in the z direction is different. Thus, the resistivity in a direction parallel to the plane of the formation (i.e., the x-y plane) is often known as the horizontal resistivity, RH, and the resistivity in the direction perpendicular to the plane of the formation (i.e., the z direction) is often known as the vertical resistivity, RV. The index of anisotropy, is defined as η=[RV/RH]1/2.
As a further complication to measuring formation resistivity, boreholes are generally not perpendicular to formation beds. The angle between the axis of the well bore and the orientation of the formation beds (as represented by a vector normal to the formation bed) has two components. These components are the dip angle and the strike angle. The dip angle is the angle between the borehole axis and the normal vector for the formation bed. The strike angle is the direction in which the boreholes axis “leans away from” the normal vector. (These will be defined more rigorously in the detailed description.)
Electromagnetic resistivity logging measurements are a complex function of formation resistivity, formation anisotropy, and the formation dip and strike angles, which may all be unknown. Moreover, engineers often rely on simplified models to interpret the measurements in a suitably prompt manner. Logging tools that fail to account for each of the unknown parameters and differences between the model and the operation of the “real world” tool may provide measurement quality that is less than ideal. Conversely, tools that account for each of these factors will provide improved resistivity measurements. Moreover, tools that are able to provide dip and strike measurements along with azimuthal orientation information, can be used for geosteering.
It should be understood, however, that the specific embodiments given in the drawings and detailed description below do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill to discern the alternative forms, equivalents, and other modifications that are encompassed in the scope of the appended claims.